Can we offer Qurbaani (animal sacrifice) on the day of Eid-ul-Adha on behalf of our deceased relatives or ancestors?

Q: Is it permissible to sacrifice an animal and pass the reward to a deceased relative?
A: There are two aspects: 1) to make a voluntary sacrifice on behalf of any person e.g. Rasulullah (Sallallaahu Alayhi Wasallam), a relative, etc. This is permissible, the person will get the reward of the sacrifice. However, one must discharge his obligation of sacrifice separately. The sacrifice on behalf of any other person will not suffice for one's own obligatory sacrifice.
2) To make one's compulsory sacrifice and thereafter make an intention of giving the reward to the deceased. In such a case, the compulsory sacrifice of the person will be discharged.

and Allah Ta'ala Knows Best

Mufti Ebrahim Desai